On Kalman, H∞ and H2 target tracking: probability of target escape

This paper considers the Kalman, H_∞ and H₂ continuous time, steady state, target tracking problem. The target escape criteria is examined, in particular the probability that the position estimate will sufficiently degrade causing the target to be outside the radar beam width. Analytical expressions for the probability of target escape are developed not only to compare the performance of the various filters, but also as a design tool to meet tracking specifications. It is shown that the Kalman and H₂ trackers have a lower probability of escape than the H_∞ tracker when the target manoeuvrability is Gaussian and within the tracker design setting. Conversely, the H_∞ process generally has a lower probability of escape than the Kalman and H₂ trackers when the target manoeuvrability is a pulse acceleration